A critical step in self-motion perception and spatial awareness is the integration of motion cues from multiple sensory organs that individually do not provide an accurate representation of the physical world. One of the best-studied sensory ambiguities is found in visual processing, and arises because of the inherent uncertainty in detecting the motion direction of an untextured contour moving within a small aperture. A similar sensory ambiguity arises in identifying the actual motion associated with linear accelerations sensed by the otolith organs in the inner ear. These internal linear accelerometers respond identically during translational motion (for example, running forward) and gravitational accelerations experienced as we reorient the head relative to gravity (that is, head tilt). Using new stimulus combinations, we identify here cerebellar and brainstem motion-sensitive neurons that compute a solution to the inertial motion detection problem. We show that the firing rates of these populations of neurons reflect the computations necessary to construct an internal model representation of the physical equations of motion.